Planar vector analyzer

ABSTRACT

Analyzing apparatus for determining characteristic magnitudes of a planar vector with the aid of two dividers, each of which has a pair of inputs. One of each pair receives a voltage proportional to one of the two orthogonal vector components respectively. The output voltages of the two dividers are added, and the sum is compared with a constant voltage in the input circuitry of a regulator, preferably an integral regulator, whose output voltage is applied to the other two inputs of the respective quotient forming members. The respective outputs of the two dividers are connected to trigonometric-function generating circuitry of electronic computer type which has an output voltage indicative of the phase angle of the vector.

United States Patent 1 Blaschke et al.

[ 1 Jan. 9, 1973 [541 PLANAR VECTOR ANALYZER [75] Inventors: FelixBlaschke, Erlangen;

Haken, Furth, both of Germany 22 Filed: March 17,1971 211 Appl.No.:125,131

[30] Foreign Application Priority Data 3,482,086 12/1969 Caswell....235/1 86 3,601,593 8/1971 Preston.... 235/197 X 3,305,674 2/1967Cook ....235/l89 3,457,394 7/1969 Grado ....235/186 X 3,496,565 2/1970Jenkins ..235/186 X OTHER PUBLICATIONS Primer on Analog Computation,"EAl General Purpose Analog Computation, Bulletin No. ALAC 64002, 1964.

Klaus Korn and Korn, Electronic Analog Computers, Mc- Graw-Hill BookCo., lnc., 1956, pp. 26-29.

CRC Standard Mathematical Tables, Fourteenth Edition, Chemical RubberCo., 1965, p.503.

Primary Examiner-Malcolm A. Morrison Assistant Examiner-Jerry SmithAttorney-Curt M. Avery, Arthur E. Wilfond, Herbert L. Lerner and DanielJ. Tick 57 ABSTRACT Analyzing apparatus for determining characteristicmagnitudes of a planar vector with the aid of two dividers, each ofwhich has a pair of inputs. One of each pair receives a voltage proportional to one of the two orthogonal vector components respectively.The output voltages of the two dividers are added, and the sum iscompared with a constant voltage in the input circuitry of a regulator,preferably an integral regulator, whose output voltage is applied to theother two inputs of the respective quotient forming members. Therespective outputs of the two dividers are connected totrigonometric-function generating circuitry of electronic computer typewhich has an output voltage indicative of the phase angle of the vector.

7 Claims, 5 Drawing Figures DESCRIPTION OF THE INVENTION Our inventionrelates to apparatus for indicating critical data of a planar vector.Such a vector analyzer comprises two dividers or stages such as dividermodules in form of respective amplifiers with a negative feedbackconnection containing a multiplier. One output of each multiplierreceives a voltage proportional to one of the two orthogonal vectorcomponents respectively. The output voltages of the multipliers aresquared, the results added to each other, and the sum is compared with aconstant voltage in the input circuit of a preferably integralregulator, whose output voltage is applied to the other two inputs ofthe respective dividers.

A system of this type affords determinating the scalar (absolute) amountof a vector as well as two orthogonal components of a unit vector whichalways points in the direction of the vector being analyzed.

It is in many cases desired, however, to also have the vector analyzerdirectly indicate the characteristic angular coordinate, that is, thephase angle, of the vector being analyzed; and it is a principal objectof out invention to devise apparatus or systems which reliably meet thisdesideratum.

To this end, and in accordance with a feature of our invention, webasically retain the fundamental features of the above-mentioned knownvector analyzer. That is, a vector analyzer according to our invention,like those heretofore known, comprises two dividers of which each hastwo inputs. One ofthese inputs, when in operation, receives a voltageproportional to one of the two orthogonal components respectively of thevector being analyzed. Squaring means are connected to the regulatorbeing connected to the other inputs of the two dividers. In departurefrom, and in addition to, the known vector analyzers, however, weprovide an analyzer according to the present invention with a functiongenerator network which comprises trigonometric-function. The generatingcircuitry which is connected to the respective outputs of the dividersand furnishes an output voltage proportional to the phase angle of thevector.

According to another, more specific feature of our invention, theoutputs of the respective two dividers are connected with the respectivefirst inputs of two multipliers, the difference between whose outputvoltages is supplied to an integrator which has its output voltageimpressed upon thetwo other inputs of the multipliers through asine-function generator and a cosine-function generator, respectively.

According to another, alternative feature of our invention, the outputvoltage of one of the dividers, added to a constant voltage magnitude ofa square-root function generator, after the constant voltage magnitudeinsert is supplied, and the output magnitude of this function generatoris supplied, in dependence upon the polarity of the other divider,either directly or through a reversing amplifier to an arcussine-function generator.

According to still another, alternative feature of our invention, theoutput signal of the one divider is supplied to the dividend input of afurther divider and the output signal of the other divider, in additionto a constant voltage, is supplied to the divisor input of theadditional divider. The output of the latter divider is connected withthe input of an arcus-tangent function generator.

According to a further feature of our invention, a technologicallysimple realization of the function generators, using either anarcus-sine or an arcus-tangent function generator, consists in havingthe function generators constituted by electronic amplifiers in hoseinput or negative feedback circuits there are provided one or morepre-biased threshold diodes.

The forgoing and further objects, advantages and features of ourinvention, said features being set forth in the claims annexed hereto,will be apparent from, and mentioned in, the following description ofembodiments of the invention illustrated by way of example in theaccompanying drawing, in which:

FIG. 1 is an explanatory diagram relating to the characteristic data ofa vector;

FIG. 2 is a logic and circuit diagram of another embodiment whichpermits selectively operating with a sine-function generator and acosine-function generator and an arcus-cosine function generator;

FIG. 3 shows a vector analyzer provided with sine and cosine-functiongenerators;

FIG. 4 is a schematic diagram of another embodiment equipped with anarcus-tangent function generator; and

FIG. 5 is a circuit diagram of a modified detail applicable in any oftheembodiments of FIGS. 2 to 4.

The same reference characters are applied in all illustrations tocorresponding items, respectively.

Relative to the terminology used in this specification and to the typeof block diagrams shown in the accompanying drawings, reference may behad to Feedback Control Systems" by Gille, Pelegrin and Decauline,McGraw-Hill Book Co., New York, 1959, pages 7 to 22 and 771; also toAnalysis of Feedback Control Systems" by Bruns and Saunders, McGraw-HillBook Co, New York, i955 pages 1 to 6, 208 and 226; and'to ElektronischeAnalogiegeraete by Dietrich Ernst, published in the German periodicalRegelungstechnik, Vol.6, I958, Nos 3 to 6,

The orthogonal coordinate system shown in FIG. 1 with an abscissa axis rand the ordinate axisj represents a planar vector A which is identifiedby two orthogonal vector components Al and A2. In many technologicalproblems, particularly in the area of electrical engineering, avectorial magnitude is predetermined or given in this form. This is thecase, for example, when representing a rotary-field indicator inelectrical rotating-field machines. Our invention solves the problem toobtain from the two vector components A] and A2 a magnitude that isproportional to the phase angle a of the vector A. The vector analyzeraccording to the invention illustrated in FIG. 2 affords selectively anoperation in two different ways, depending upon the selected setting oftwo switches orjumpers l2 and 13.

The upper portion of FIG. 2 shows a block diagram of the vector analyzerproper. It comprises two dividers 1 and 2. The dividend inputs areconnected through respective terminals 3 and 4 with voltages A1 and A2which are proportional to the orthogonal components of the vector A(FIG. 1). The outputs of the dividers 1 and 2 are squared with the aidof two multipliers 5 and 6 whose output magnitudes are added to eachother in a mixer member 7. The input of this mix er member 7 is furthersupplied in the subtractive sense with a constant voltage E. Thisvoltage is to have the magnitude 1, that is, this voltage is a so-calledunit voltage. The output of the mixing member 7 is applied to anintegrator 8 in the form of a Pl-regulator whose output is connectedwith the divisor inputs of the dividers l and 2. For stability reasons,the integrator is given a stop or limit means which limit the integratoroutput voltage unilaterally to zero so that it will conductonly-positive values of this output voltage. A properly poled diode maybe used as such a unilateral stop.

Denoting the output magnitude of the Pl-regulator 8 by x and consideringthe known fact that the output magnitude of a Pl-regulator will ceasechanging only 1 when the sum of its input magnitudes vanishes, then theregulating circuit so far described reaches its stationary, i.e.equalizer state when the following equation is met:

;Under these conditions, the output magnitude of the integrator 8corresponds exactly to the scalar (absolute) amount A of the vector A.In this automatically occurring stationary state, the voltages at therespective outputs of the dividers l and 2 have the magnitudes A IIAIcosaand A IA =sina Consequently, voltages appear at the output terminals9, l0 and 11 of the vector analyzer which are proportional respectivelyto the scalar amount of the vector A (terminal 9), to the sine of itsphase angle a (terminal 10) and to the cosine ofits phase angle a(terminal 1 l When the outputs of the dividers l and 2, in theillustrated vertical position of the two switching bridges or jumpers l2and 13 are connected with the circuitry shown at the left of a brokenline I, then the first inputs of two multipliers 14 and 15 are suppliedwith voltage proportional to the sine and the cosine respectively of thephase angle a. The outputs ofthe two multipliers l4 and 15 aresubtracted from each other in a mixer member 16. The output of themember 16 which, like the mixer member 7, may consist of an addingamplifier, is connected to the input of an integrator 17 which, in turn,supplies voltage to the second input of the multiplier 14 through acosine-function generator 18 and to the second input of the multiplier15 through a sinefunction generator 19. Denoting the output magnitude ofthe integrator 17 by y and again taking into account that the integratoroutput magnitude will stop changing only when its input magnitudevanishes, then the stationary stage automatically set up as a result ofthe regulation, satisfies the condition sin a cos y cos a sin y 0. Thisrequirement is met only when y a. Hence, the voltage at the outputterminal 20 is directly proportional to the phase angle a.

When the switches orjumpers l2 and 13 are moved to the horizontalpositions indicated by broken lines in FIG. 2, then the circuitryillustrated at the right of the broken line I becomes effective andlikewise operates to determine the phase angle a. The output magnitudeof the divider 1 is added to a constant unit voltage E, having a value1, the addition being effected in the mixer member 21. The resulting sumvoltage is supplied to a proportional amplifier 22 having an'amplifyingfactor or gain of 0.5. In practice, the mixer member 21 may beconstituted by the input circuitry of the amplifier 22, which in thiscase is designed as an adding amplifier.

The other mixing member 7 or 16 shown in FIG. 2 may analogously beincluded in the input circuitry of the next following circuit members.The output voltage of the amplifier 22 is supplied to a square-rootfunction generator 23 that is, the output magnitude a and the inputmagnitude e of the function generator 23 are related as a VZ'Due to theknown relation between the cosine of an angle and the cosine of thedoubled angle, the voltage appearing at the output of the functiongenerator 23 is proportional to' cos 01/2 and always has a positivepolarity or sign.

The output of the other divider 2, at which the voltage proportional tothe sine of the phase angle 0: appears, has its input sign connected toa limit value indicator 24 whose output provides a constant positivevoltage when the output voltage of the divider is positive, whereas theoutput voltage of the limit value .in-, dicator 24 disappears if theoutput voltage from the divider 2 is negative. The output signal of thelimit value indicator 24 directly indicates a switch 25 and acts througha reversing stage 26 to actuate another switch 277 The reversing stage26 is supposed to have a positive constant signal at its output, whenthe input voltage is zero, whereas the output voltage of stage 26 iszero as long as its input voltage has a value differing from zero. Ifthe limit value indicator has two antivalent outputs, then such anoutput can assume the function of the reversing stage. If one looks atthe state in which the output voltage of the divider 2 has a positivevalue, it will be seen that under this condition the switch 25 isactuated by the output voltage of the limit value indicator 24.

Depending upon the polarity of the output signal of the divider 2, thatis, depending upon the sign of the function sine a, the output magnitudeof the square-root function generator 23 is connected either directlythrough the switch 25 or through a polarity reversing amplifier 28 tothe input of an arcus-cosine function generator 29. This affordsrepresenting by a corresponding voltage, the angle 01/2 throughout arange of 0 to or when doubling the output magnitude of the functiongenerator 29 with the aid of an amplifier 30, the phase angle a canthusbe represented by a voltage throughout a range of 0 to 360. Hence, withthis modification of the apparatus, the voltage directly proportional tothe phase angle a can be taken from the output terminal 3].

Modules known from and available for the analogue computing techniqueare applicable for realizing the arcus-cosine function generator 29 inthe form of hardware, and the circuitry or hardware needed for the otherfunction generators l8, l9 and 23. The function generator 29 has betweenits output magnitude a and its input magnitude e the relationgraphically indicated in the block diagram, that is, a arc cos e. Thesemodules, for example, comprise electronic amplifiers with severalpre-biased threshold diodes in the input or negative feedback circuit.With an increasing input or output voltage, the individual biasedthreshold diodes, such as Zener diodes, will sequentially conduct andthus change the inclination of the amplifier characteristic to thedesired extent. By using a sufficiently large number of such thresholddiodes, the desired function can be approached at any desired degree ofaccuracy. It is further possible to realize in practice the multipliers5 and 6 by electronic amplifiers with biased threshold diodes in theinput circuit, taking into account that the relation between the outputmagnitude a and the input magnitude e in this case is a 2 A moredetailed illustration of circuitry for the portion of the equipmentcomprising the elements I through 8 (FIG. 2) is shown in FIG. 3. Thereference characters of FIG. 3 correspond to those of FIG. 2. In FIG, 3,the input terminals 3 and 4 are impressed by two voltages correspondingto the respective orthogonal components of the vector. The voltagesapplied to the input terminals 3 and 4 are supplied to respectiveamplifiers 34 and 35 which are feedbackconnected through respectivemultipliers 32 and 33 and which under no-load conditions exhibit a highamplifying gain. The feedback-connected amplifiers 35 and 34 operate asdividers.

The output voltages of the amplifiers 34 and 35 are squared in twofurther multipliers 5 and 6, respectively. The output voltages of themultipliers 5 and 6, together with a constant direct voltage of amagnitude N are applied to the input of the adding amplifier 7 whichacts upon the input of a PI-regulator 8. A limit member 36 is providedat the output of the PI-amplifier, for example, in the form of aconventional limiting diode, such a Zener diode, by which the outputvoltage of the regulator is unilaterally limited to zero.

The output voltage of the Pl-amplifier 8 acts upon the other inputs ofthe two multipliers 32 and 33. At the output voltage 9, as alreadyexplained with reference to FIG. 2, there appears a voltage which isproportional to the scalar amount of the vector A formed by twoorthogonal components A], A2 whose amounts correspond to the voltagesapplied to the input terminals 3 and 4 of the equipmenL The outputvoltages of the amplifiers 34 and 35 are supplied to two negativelyfeedback-connected reversing amplifiers 37 and 38 whose feedbackresistances relative to their input resistance have the ratio IzN. Underthese conditions, there appear at the terminals 10 and 11 respectivevoltages that correspond to the sine and the cosine of the phase angle aand which may be looked upon as being the component of a unit vectorwhich always points in the direction of the vector A.

The modification shown in FIG. 3 has the advantage that it offers a freeselection of the constant voltage supplied to the adding amplifier 7,provided the departure of this voltage from the value I is taken intoaccount by a correspondingly dimensioned resistance ratio between inputand negative feedback resistances in the reversing amplifiers 38 and 37.

The embodiment of FIG. 4 is only partially illustrated by assuming thatthe non-illustrated portion corresponds to the corresponding portion ofFIG. 2. That is, the terminals 39 and 40 of FIG. 4 are connected, as inthe embodiment of FIG. 2, to the outputs of the respective dividers land 2, so that a voltage appears at the terminal 39 which corresponds tothe'sine of the phase angle 0:, whereas the voltage at the terminal 40corresponds to the cosine of the same angle. A constant unit voltagehaving a magnitude of 1 is added in a mixing member 41, and the sum issupplied to the divisor input of the divider 42 whose dividend input isconnected to the terminal 39. I

A voltage appears at the output of the divider 42 which is proportionalto tan 01/2. This systemis further provided with an arcus-tangentfunction generator 43, the relation between its input magnitude e andoutput magnitude a being a arc tan e. The function generator 43 convertsthe output voltage of the divider 42 to a voltage proportional to theangle 01/2. The latter volt-.

age is amplified to twice its value in the next-following amplifier 44.Consequently, the output of the amplifier 44 is directly proportional tothe phase angle a and is available at the output terminal 45.

The modification illustrated in FIG. 4, compared I with the right-handportion of FIG. 2, has the advantage of avoiding the need for asquare-root forming function generator, which in the vicinity of thezero point can furnish only approximate function values.

FIG. 5 shows an embodiment of an amplifier with Zener diodes in anegative feedback circuit and in the 1 having two inputs of which onedivider receives when in operation a voltage proportional to one of thetwo orthogonal components respectively of the vector to be analyzed,squaring means connected to said respective dividers, adder meansconnected to said two squaring means and having an output whose voltageis proportional to the sum of the two squared voltages, at regulatorhaving comparator means for comparing said sum voltage with a constantreference voltage and having an output whose voltages is proportional tothe scalar value of the vector and which is connected to said otherinputs of said two dividers, in combination with two multipliers ofwhich each has two inputs and one of which multipliers is connected tothe output of one of said respective dividers, subtractor means havingtwo inputs connected to the respective outputs of said multipliers andhaving a subtractor output whose voltage is proportional to thedifference between two multiplier output voltages, an integratorconnected to said subtractor output and having an output voltageindicative of the vector phase angle, and trigonometric-functiongenerator means connected to the output of said integrator.

2. In a vector analyzer according to claim 1, said function generatormeans comprising a sine-function generator and a cosine-functiongenerator, said integrator having its output connected through saidrespective function generators to sad respective other inputs of saidtwo multipliers.

3. ln a vector analyzer according to claim 2, said integrator being anelectronic Pl amplifier.

4. In a vector analyzer according to claim' 1, said regulator being anintegral regulator.

'5. In a vector analyzer according'to claim 1, said function generatormeans comprising electronic amplifiers having input circuits andnegative feedback circuits, and having voltage-biased threshold diodemeans in at least one of said circuits.

6. Vector analyzer comprising two dividers each having two inputs ofwhich one divider receives when in operation a voltage proportional toone of the two orthogonal components respectively of the vector to beanalyzed, squaring means connected to said respective dividers, addermeans connected to said two squaring means and having an output whosevoltage is proportional to the sum of the two squared voltages, aregulator having comparator means for comparing said sum voltage with aconstant reference voltage and having an output whose voltage isproportional to the scalar value of the vector and which is connected tosaid other inputs of said two dividers, adding means connected to theoutput of one of said dividers for adding a constant voltage magnitude,a square-root forming function generator connected to the output of saidadding means and having a generator output voltage proportional to thesquare root of the addition result, a reversing amplifier, anarcus-cosine function generator,

and means for selectively connecting the output voltage of saidsquare-root forming generator directly and through said reversingamplifier respectively to said arcus-cosine function in dependence uponthe polarity of said other divider.

7. A vector analyzer comprising two dividers each having two inputs ofwhich one divider receives when in operation a voltage proportional toone of the two orthogonal components respectively of the vector to beanalyzed, squaring means connected to said respective dividers, addermeans connected to said two squaring means and having an output whosevoltage is proportional to the sum of the two squared voltages, aregulator having comparator means for comparing said sum voltage with aconstant reference voltage and having an output whose voltage isproportional to the scalar value of the vector and which is connected tosaid other inputs of said two dividers, adding means connected to theoutput of one of said two dividers for adding a constant voltage to theoutput signal of said one of said dividers, a further divider having adividend input and a divisor input, said dividend input being connectedto the output of said other divider, said divisor input being connectedto said adding means to receive the resulting sum voltage therefrom, andan arcus-tangent function generator having an input connected with theoutput of said further divider.

1. A vector analyzer comprising two dividers each having two inputs ofwhich one divider receives when in operation a voltage proportional toone of the two orthogonal components respectively of the vector to beanalyzed, squaring means connected to said respective dividers, addermeans connected to said two squaring means and having an output whosevoltage is proportional to the sum of the two squared voltages, aregulator having comparator means for comparing said sum voltage with aconstant reference voltage and having an output whose voltages isproportional to the scalar value of the vector and which is connected tosaid other inputs of said two dividers, in combination with twomultipliers of which each has two inputs and one of which multipliers isconnected to the output of one of said respective dividers, subtractormeans having two inputs connected to the respective outputs of saidmultipliers and having a subtractor output whose voltage is proportionalto the difference between two multiplier output voltages, an integratorconnected to said subtractor output and having an output voltageindicative of the vector phase angle, and trigonometric-functiongenerator means connected to the output of said integrator.
 2. In avector analyzer according to claim 1, said function generator meanscomprising a sine-function generator and a cosine-function generator,said integrator having its output connected through said respectivefunction generators to sad respective other inputs of said twomultipliers.
 3. In a vector analyzer according to claim 2, saidintegrator being an electronic PI amplifier.
 4. In a vector analyzeraccording to claim 1, said regulator being an integral regulator.
 5. Ina vector analyzer according to claim 1, said function generator meanscomprising electronic amplifiers having input circuits and negativefeedback circuits, and having voltage-biased threshold diode means in atleast one of said circuits.
 6. Vector analyzer comprising two dividerseach having two inputs of which one divider receives when in operation avoltage proportional to one of the two orthogonal componentsrespectively of the vector to be analyzed, squaring means connected tosaid respective dividers, adder means connected to said two squaringmeans and having an output whose voltage is proportional to the sum ofthe two squared voltages, a regulator having comparator means forcomparing said sum voltage with a constant reference voltage and havingan output whose voltage is proportional to the scalar value of thevector and which is connected to said other inputs of said two dividers,adding means connected to the output of one of said dividers for addinga constant voltage magnitude, a square-root forming function generatorconnected to the output of said adding means and having a generatoroutput voltage proportional to the square root of the addition result, areversing amplifier, an arcus-cosine function generator, and means forselectively connecting the output vOltage of said square-root forminggenerator directly and through said reversing amplifier respectively tosaid arcus-cosine function in dependence upon the polarity of said otherdivider.
 7. A vector analyzer comprising two dividers each having twoinputs of which one divider receives when in operation a voltageproportional to one of the two orthogonal components respectively of thevector to be analyzed, squaring means connected to said respectivedividers, adder means connected to said two squaring means and having anoutput whose voltage is proportional to the sum of the two squaredvoltages, a regulator having comparator means for comparing said sumvoltage with a constant reference voltage and having an output whosevoltage is proportional to the scalar value of the vector and which isconnected to said other inputs of said two dividers, adding meansconnected to the output of one of said two dividers for adding aconstant voltage to the output signal of said one of said dividers, afurther divider having a dividend input and a divisor input, saiddividend input being connected to the output of said other divider, saiddivisor input being connected to said adding means to receive theresulting sum voltage therefrom, and an arcus-tangent function generatorhaving an input connected with the output of said further divider.